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Ponce, Nicolas Wilmet","submitted_at":"2017-05-10T12:17:48Z","abstract_excerpt":"We study the existence of solutions of the Dirichlet problem for the Schroedinger operator with measure data $$ \\left\\{ \\begin{alignedat}{2} -\\Delta u + Vu & = \\mu && \\quad \\text{in } \\Omega,\\\\ u & = 0 && \\quad \\text{on } \\partial \\Omega. \\end{alignedat} \\right. $$ We characterize the finite measures $\\mu$ for which this problem has a solution for every nonnegative potential $V$ in the Lebesgue space $L^p(\\Omega)$ with $1 \\le p \\le N/2$. The full answer can be expressed in terms of the $W^{2,p}$ capacity for $p > 1$, and the $W^{1,2}$ (or Newtonian) capacity for $p = 1$. 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